Inherent Variability in the Kinetics of Autocatalytic Protein Self-Assembly

Abstract

In small volumes, the kinetics of filamentous protein self-assembly is expected to show significant variability, arising from intrinsic molecular noise. This is not accounted for in existing deterministic models. We introduce a simple stochastic model including nucleation and autocatalytic growth via elongation and fragmentation, which allows us to predict the effects of molecular noise on the kinetics of autocatalytic self-assembly. We derive an analytic expression for the lag-time distribution, which agrees well with experimental results for the fibrillation of bovine insulin. Our expression decomposes the lag-time variability into contributions from primary nucleation and autocatalytic growth and reveals how each of these scales with the key kinetic parameters. Our analysis shows that significant lag-time variability can arise from both primary nucleation and from autocatalytic growth and should provide a way to extract mechanistic information on early-stage aggregation from small-volume experiments.

What Can the Kinetics of Amyloid Fibril Formation Tell about Off-pathway Aggregation?

“…2c). Characteristic but not exclusive of HEWL aggregation, the low reproducibility of the results further prevents definitive conclusions to be made without testing wider ranges of protein concentrations and numerous other replicates (40,43,47,48). The previously reported formation of intermediate and off-pathway species during amyloid fibrillization of lysozyme should, however, produce atypical kinetic signatures and explain in part the poor reproducibility indexes.…”

Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly

“…Even though different secondary processes lead to very different size distributions of fibrils, they affect the total polymerised mass, represented here by the quantity of the species Y, in a qualitatively similar way in that they provide acceleration of growth through positive feedback. In particular, we expect our model to behave qualitatively similarly to the mechanistic model described in [14], which includes nucleation, polymerization, and fragmentation as a self-accelerating process.…”

“…Even though different secondary processes lead to very different size distributions of fibrils, they affect the total polymerised mass, represented here by the quantity of the species Y, in a qualitatively similar way in that they provide acceleration of growth through positive feedback. In particular, we expect our model to behave qualitatively similarly to the mechanistic model described in [14], which includes nucleation, polymerization, and fragmentation as a self-accelerating process.Stochastic Evolution. Any given pair of monomers reacts together by Reaction (1) at rate α/V 2 A , whereas for a given pair of monomer/polymerized monomer reacts by Reaction (2) at rate β/V initial number of monomers and the random variable describing the number of monomers remaining at time t is denoted by X V (t).…”

“…Amyloid growth experiments typically follow the appearance of amyloid arXiv:1510.03982v1 [q-bio.CB] 14 Oct 2015 2 aggregates or the depletion of monomers as function of time, yielding information regarding the rate of the exponential growth and the length of the lag phase under different protein concentrations at fixed volumes. A hitherto overlooked piece of information that can be derived from these kinetic experiments is the observed variation between experimental repeats, which may hold the key to understanding the early rare nucleation events of amyloid formation [11,[14][15][16]. However, current deterministic models cannot describe variability, thus, unable to address whether the observed variations in lag phase length reflect subtle experimental differences between the replicates, contributions from the stochastic nature of the nucleation mechanism, or a combination of both factors.…”

“…Our model further informed the need for new mechanistic steps or experimental interpretation of the large observed variations in the lag time lengths. Thus, the variation seen in the kinetic traces must be taken into account in addition to the concentration dependent behaviour of the kinetic traces in evaluating and developing mechanistic understanding of amyloid protein assembly processes.While our model design was not aimed at describing the reality of any specific amyloid forming system with all of their individual associated complexities, our design by pursuing maximum simplicity are complementary to mechanistic approaches such as in [10,11,14] in capturing global properties of amyloid assembly. Thus, our method allows for a rigorous theoretical treatment and understanding, and provides a basis for model selection on stochastic 'minimal models', each of these models being the condensation of a family of possible stochastic mechanistic models, closer to reality but for which analytical formulae are out of reach.…”